On the M-eigenvalue estimation of fourth-order partially symmetric tensors

Haitao Che; Haibin Chen; Yiju Wang

doi:10.3934/jimo.2018153

Article Contents

2020, Volume 16, Issue 1: 309-324. Doi: 10.3934/jimo.2018153

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On the M-eigenvalue estimation of fourth-order partially symmetric tensors

1.
School of Mathematics and Information Science, Weifang University, Weifang Shandong, 261061, China
2.
School of Management Science, Qufu Normal University, Rizhao Shandong, 276826, China

* Corresponding author: Haitao Che
* Corresponding author: Haitao Che

Received: December 31, 2017

Revised: April 30, 2018

Early access: September 2018

Published: October 2019

This project is supported by the Natural Science Foundation of China (11401438, 11671228, 11601261, 11571120), Shandong Provincial Natural Science Foundation (ZR2016AQ12), Project of Shandong Province Higher Educational Science and Technology Program(Grant No. J14LI52), and China Postdoctoral Science Foundation (Grant No. 2017M622163, 2018T110669).

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Abstract

In this article, the M-eigenvalue of fourth-order partially symmetric tensors is estimated by choosing different components of M-eigenvector. As an application, some upper bounds for the M-spectral radius of nonnegative fourth-order partially symmetric tensors are discussed, which are sharper than existing upper bounds. Finally, numerical examples are reported to verify the obtained results.

Keywords:

M-eigenvalue,
Z-eigenvalue,
fourth-order partially symmetric tensors,
spectral property,
localization theorem,
nonnegative tensors.

Mathematics Subject Classification: Primary: 15A06, 74B20; Secondary: 47J25.

Citation:

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Figure 1. The comparisons of $ \Gamma(\mathcal{C})$, $ \mathcal{L}(\mathcal{C})$, $ \mathcal{M}(\mathcal{C})$ and $ \mathcal{N}(\mathcal{C})$

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Figure 2. The comparisons of $ \Gamma(\mathcal{C})$, $ \mathcal{L}(\mathcal{C})$ and $ \mathcal{M}(\mathcal{C})$

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Figure 3. The comparisons of $ \Gamma(\mathcal{C})$, $ \mathcal{L}(\mathcal{C})$ and $ \mathcal{M}(\mathcal{C})$

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